Re: Constrained Min, non-linear

• To: mathgroup at smc.vnet.net
• Subject: [mg4517] Re: Constrained Min, non-linear
• From: Stephen P Luttrell <luttrell at signal.dra.hmg.gb>
• Date: Fri, 2 Aug 1996 02:22:42 -0400
• Organization: Defence Research Agency, Malvern
• Sender: owner-wri-mathgroup at wolfram.com

```Stefan Wolfrum wrote:
>...DELETIA...
> Where is f(x,y)=x^2+y^2 minimal, if x and y are
> constrained to abs(x+y)=1 ?

Try the following (this is long-winded for this particular
problem because the solution is geometrically obvious):

(* define the basic functions *)
f[x_, y_] := x^2 + y^2;
g[x_, y_] := x + y;
(* differentiate using a Lagrange multipler *)
dx = D[f[x,y] + a g[x,y], x];
dy = D[f[x,y] + a g[x,y], y];
(* find the stationary point *)
soln = Solve[{dx==0, dy==0}, {x,y}];
(* find values of a that satisfy Abs[g[x,y]]==1 at the stationary point *)
g0 = g[x, y] /. soln[[1]];
a1 = Solve[g0 == 1, a];
a2 = Solve[g0 == -1, a];
(* finally generate the 2 solutions *)
soln /. a1
soln /. a2

--
Dr Stephen P Luttrell                  luttrell at signal.dra.hmg.gb